Beyond the Grid: GLRT-Based TomoSAR Fast Detection for Retrieving Height and Thermal Dilation

The Tomographic Synthetic Aperture Radar (TomoSAR) technique is widely used for monitoring urban infrastructures, as it enables the mapping of individual scatterers across additional dimensions such as height (3D), thermal dilation (4D), and deformation velocity (5D). Retrieving this information is crucial for building management and maintenance. Nevertheless, accurately extracting it from TomoSAR data poses several challenges, particularly the presence of outliers due to uneven and limited baseline distributions. One way to address these issues is through statistical detection approaches such as the Generalized Likelihood Ratio Test, which ensures a Constant False Alarm Rate. While effective, these methods face two primary limitations: high computational complexity and the off-grid problem caused by the discretization of the search space. To overcome these drawbacks, we propose an approach that combines a quick initialization process using Fast-Sup GLRT with local descent optimization. This method operates directly in the continuous domain, bypassing the limitations of grid-based search while significantly reducing computational costs. Experiments conducted on both simulated and real datasets acquired with the TerraSAR-X satellite over the Spanish city of Barcelona demonstrate the ability of the proposed approach to maintain computational efficiency while improving scatterer localization accuracy in the third and fourth dimensions.